I'm working a problem, attempting to find a income tax rate that will change depending on the gross paycheck amount. Some data points:
$800 gross = 11% taxed
$1500 gross = 16% taxed
$2000 gross = 20% taxed
How would I go about finding the relationship between the gross paycheck amount and the percentage taxed? Beyond that as well, how will I then be able to apply that relationship mathematically in order to obtain other data points (\$1000 gross paycheck, $500, etc...) and get an accurate tax percentage for them as well? I have a feeling it'll be an answer lying somewhere in the statistics field, but I'm no math expert.
As Listing says, there is no unique solution. One approach would be to plot tax paid against gross income, draw a smooth curve and estimate any interpolated values.
So for a gross income of $\$1000$, tax might be about $\$130$ i.e. about 13%.
If you are feeling brave, you might try to extrapolate outside the points you know (the tax on a gross income of $\$0$ might be $\$0$), but you are more likely to be wrong.